I don't agree that they serve the same purpose; shorting is not the same as buying a put and the two only behave similarly in a very narrow and limited sense that isn't particularly practical. Yes in some circumstances money is gained if the price of a stock decreases with both a short and a put, but the risk profile, timing and cost are quite distinct.

Furthermore it's absolutely possible and in many circumstances likely that the price of a put decreases even if the underlying stock's price decreases, for example if the volatility also decreases.

I don't think many informed individuals treat shorting stock the same way they treat buying puts nor do they attempt to accomplish the same purpose.

I didn't say they were the same, but they serve the same purpose. Buying a put is a long volatility and short underlying position. You can mitigate the effect of volatility with spreads. But the directionality of the position is what you're buying with a put, you're buying delta within a certain time frame. And as I said, the risk profile of put or well constructed spread is better than plain shorting which has unlimited downside.